At present the possible existence of planets around the stars of a close binary
system is still matter of debate. Can planetary bodies form in spite of the
strong gravitational perturbations of the companion star? We study in this
paper via numerical simulation the last stage of planetary formation, from
embryos to terrestrial planets in the α Cen system, the prototype of
close binary systems. We find that Earth class planets can grow around
α Cen A on a time-scale of 50 Myr. In some of our numerical models the
planets form directly in the habitable zone of the star in low eccentric orbits.
In one simulation two of the final planets are in a 2:1 mean motion resonance
that, however, becomes unstable after 200 Myr.
During the formation process some
planetary embryos fall into the stars possibly altering their metallicity.

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